Bounds for Moments of Dirichlet L-functions of fixed modulus on the critical line

Key Points

• Sharp lower bounds for the moments of Dirichlet L-functions were established for all real k ≥ 0, ensuring effective range limits.
• Upper bounds were identified for the range of k from 0 to 1, offering critical insights into the behavior of these number-theoretic functions.
• The study focuses on the family of Dirichlet L-functions for a fixed prime modulus, highlighting the significance of the modulus in their analysis.
• This research provides essential bounds that expand understanding of moments for Dirichlet L-functions along the critical line in number theory.